scholarly journals Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1414
Author(s):  
Loris Di Di Cairano ◽  
Matteo Gori ◽  
Marco Pettini
Keyword(s):  
Phase Transitions ◽  
Phase Space ◽  
Total Energy ◽  
Sufficient Conditions ◽  
Physical Systems ◽  
Analytical Step ◽  
Definition Of ◽  
Open Question ◽  
Sufficiency Conditions ◽  
Topological Changes

Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy.

A Philosophical Analysis To Uncover The Meaning And Terminology Of Person In Indonesian Criminal Law Context

2017 ◽  
Vol 1 (1) ◽  
pp. 56
Author(s):  
Nani Mulyati ◽  
Topo Santoso ◽  
Elwi Danil
Keyword(s):  
Criminal Law ◽  
Sufficient Conditions ◽  
Criminal Code ◽  
Legal Person ◽  
Philosophical Approach ◽  
Legal Personality ◽  
Legal Subject ◽  
Long Time ◽  
Definition Of ◽  
Broad Meaning

The definition of person and non-person always change through legal history. Long time ago, law did not recognize the personality of slaves. Recently, it accepted non-human legal subject as legitimate person before the law. This article examines sufficient conditions for being person in the eye of law according to its particular purposes, and then, analyses the meaning of legal person in criminal law. In order to do that, scientific methodology that is adopted in this research is doctrinal legal research combined with philosophical approach. Some theories regarding person and legal person were analysed, and then the concept of person was associated with the accepted definition of legal person that is adopted in the latest Indonesian drafted criminal code. From the study that has been done, can be construed that person in criminal law concerned with norm adressat of the rule, as the author of the acts or omissions, and not merely the holder of rights. It has to be someone or something with the ability to think rationally and the ability to be responsible for the choices he/she made. Drafted penal code embraces human and corporation as its norm adressat. Corporation defined with broad meaning of collectives. Consequently, it will include not only entities with legal personality, but also associations without legal personality. Furthermore, it may also hold all kind of collective namely states, states bodies, political parties, state’s corporation, be criminally liable.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 730
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Initial Time ◽  
Lipschitz Stability ◽  
Comparison Results ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Definition Of

In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

The 3 C's of the Circular Economy for Food. A conceptual framework for circular design in the food system

2021 ◽  
Author(s):  
Franco Fassio
Keyword(s):  
Sustainable Development ◽  
Conceptual Framework ◽  
Circular Economy ◽  
Food System ◽  
Raw Material ◽  
Starting Point ◽  
Development Goals ◽  
Definition Of ◽  
Open Question ◽  
Circular Design

Food, the basic connecting unit of all the UN's Sustainable Development Goals, plays a crucial role in the ecological transition towards a circular economic paradigm. This paper takes scientific considerations as a starting point in order to contribute to the definition of a theoretical-operational framework in which to grow the Circular Economy for Food. This is a still-open question in a sector of the circular economy that is emerging as vital to sustainable development. The 3 C's of Capital, Cyclicality and Co-evolution offer a systemic, holistic vision of the food system's role. Within this conceptual framework, the designers can find the main boundaries of the system, within which to express their creativity. The aim must be to avoid damaging relationships with the best supplier of raw material known to humanity (Nature), respecting planetary boundaries and at the same time offering a fair space to civil society.

scholarly journals Local and global extrema for functions of several variables

1980 ◽  
Vol 29 (3) ◽  
pp. 362-368 ◽  
Author(s):  
Bruce Calvert ◽  
M. K. Vamanamurthy
Keyword(s):  
Critical Point ◽  
Local Minimum ◽  
Global Minimum ◽  
Sufficient Conditions ◽  
Subject Classification ◽  
General Function ◽  
Several Variables ◽  
Open Question

AbstractLet p: R2 → R be a polynomial with a local minimum at its only critical point. This must give a global minimum if the degree of p is < 5, but not necessarily if the degree is ≥ 5. It is an open question what the result is for cubics and quartics in more variables, except cubics in three variables. Other sufficient conditions for a global minimum of a general function are given.1980 Mathematics subject classification (Amer. Math. Soc.): 26 B 99, 26 C 99.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 630
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Nonlinear Alternative ◽  
Contractive Map ◽  
Fractional Differential ◽  
Definition Of

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

scholarly journals Generalized Timelike Mannheim Curves in Minkowski Space-Time

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Akyig~it ◽  
S. Ersoy ◽  
İ. Özgür ◽  
M. Tosun
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Space Time ◽  
Necessary And Sufficient Conditions ◽  
Minkowski Space Time ◽  
Mannheim Curve ◽  
Definition Of ◽  
Necessary And Sufficient

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

scholarly journals The Total Energy and Momentum Stored in a Particle

2017 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Eyal Brodet
Keyword(s):  
Total Energy ◽  
Special Relativity ◽  
Decay Time ◽  
Rest Mass ◽  
Minimum Time ◽  
Mass Energy ◽  
Light Velocity ◽  
Extra Energy ◽  
Definition Of ◽  
Energy And Momentum

In this paper we reconsider the conventional expressions given by special relativity to the energy and momentum of a particle. In the current framework, the particle's energy and momentum are computed using the particle's rest mass, M and rest mass time, t_m=h/M c^2  where t_m has the same time unit as conventionally used for the light velocity c. Therefore it is currently assumed that this definition of time describes the total kinetic and mass energy of a particle as given by special relativity. In this paper we will reexamine the above assumption and suggest describing the particle's energy as a function of its own particular decay time and not with respect to its rest mass time unit. Moreover we will argue that this rest mass time unit currently used is in fact the minimum time unit defined for a particle and that the particle may have more energy stored with in it. Experimental ways to search for this extra energy stored in particles such as electrons and photons are presented.

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